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Surface operation of a GPS receiver also requires 4 satellites unless your 
geodetic height is accurately known. If at sea level, your orthometric height 
is roughly known but the geoidal undulation can be up to 100 metres or so, so 
you'll need that to get your geodetic height. Any error in assumed geodetic 
height will map to some degree into the horizontal coordinates.

Some RAIM techniques require 6 satellites. For a bit of additional info on 
RAIM look here (and possibly consult "Further Reading":
http://gge.unb.ca/Resources/gpsworld.march99.pdf

-- Richard Langley 

On 2013-03-20, at 3:32 AM, Gary LaPook wrote:

> RAIM (Receiver Autonomous Integrity Monitoring) is probably not known to 
surface navigators but is vitally important to pilots who end up flying GPS 
instrument approaches to the runway and descending to within 100 feet of the 
ground without being able to see anything outside the plane because the plane 
is inside the clouds. The GPS must provide accurate information to ensure 
that the plane is descending along a safe path that lines the plane up with 
the unseen runway. There must also be a way to ensure that the system is 
working properly so that the pilot can be sure that the GPS is providing the 
required level of accuracy and this is where RAIM comes in. 
> 
> An airborne GPS requires signals from four satellites to determine a 
position while surface GPS only requires three. RAIM then uses the signal 
from a fifth satellite to check the accuracy of the GPS position and if it is 
not accurate enough for safe flight warns the pilot. 
> 
> I have suggested that a celestial navigator take a two body fix and then use 
the third LOP just to check the accuracy of that two body fix and to catch 
any errors, just like RAIM. See:
> 
> http://en.wikipedia.org/wiki/Receiver_Autonomous_Integrity_Monitoring
> 
> http://www.askacfi.com/5429/when-is-raim-required.htm
> 
> 
> gl
> 
> Go to page 76 of the PDF of the AIIM.  http://www.faa.gov/air_traffic/publications/ATpubs/AIM/aim.pdf
> 
> 
> 
> 
> --- On Tue, 3/19/13, Byron Franklin  wrote:
> 
> From: Byron Franklin 
> Subject: [NavList] Observing Celestial bodies
> To: garylapook---net
> Date: Tuesday, March 19, 2013, 5:34 PM
> 
> Byron: A person who understands the nature of errors avoids many pitfalls. 
Thus the magnitude of the error of individual lines of position is not a 
reliable indication of the size of the error of the fix
> obtain from them. The size of the triangle formed by three lines of position 
has often been used as a guide to the accuracy of the fix, although a large 
triangle might be the result of a large constant error if the objects 
observed are equally spaced in azimuth. On the other hand, two lines of 
position with small errors might produce a fix having mach larger errors if 
the line crosses at a small angle.�Bowditch. 
> Byron �Let us use a large angle nearest to 90 degrees for accuracy for the best fix�
> What I have seen and read in the course books on Navigation is bad for the beginner.
> The real needed information is not complete, sure you can get the job done using what is in the books, 
> but if you want to get the best fix you must understand how to think, the books won�t help.
> In my Franklin Piloting Technique the navigator takes 3 Navaids two Navaids 
are selected for the fix. In this case the two closer Navaid become the ships 
position. The farthest Navaid become an indicator of accuracy and can give a 
direction + or � and the amount of error in degrees the Navigator can solve 
compass error and get the good fix. It has been taught at navy schools 
including the Naval Academy as well the Navigation Bowditch and Chief 
Quartermaster Manuel.
> Taking a celestial round of stars has some similarity in that a round of 
sights with near to ninety degrees cannot be improved upon as far as the 
angle of cut, but you must have an indicator as to accuracy, the same as the 
piloting technique. You must add another star or more. They will not improve 
the fix position, but can give a clue to the accuracy. If they do not support 
the near 90 degree best fix, chose the next best near 90 intersection. Often 
you will see an example in the book of three stars one with East �West Line 
of position No. two with a 045-225 No 3 with 000-180 and the fix in the 
center of the three. The 90 degree position should be the best choice. The 
present books will pick the center of the three lines as the idea choice! 
This is alright, I will not argue about this, but for myself I will pick the 
best intersection near 90 degree as my fix. I will be correct more times than 
the book. We are nit picking, but my experience on board a Radar Picket 
Liberty Hull for 5 years using sextant and loran A for fixes while tracking 
aircraft coming to the US shore. I had to get ships positions by sun-lines 
and shooting stars for l fixes for reference tracking point at sea I had 27 
years of at sea Navigation and Navigation teaching at Naval schools 
> My third ship a Liberty Hull with it old bad equipment and lack of on board knowledge taught me well.
> The encluded is from my old Navy QM book on Navigation. 
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| Richard B. Langley                            E-mail: lang@unb.ca         |
| Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/ |
| Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142   |
| University of New Brunswick                   Fax:      +1 506 453-4943   |
| Fredericton, N.B., Canada  E3B 5A3                                        |
|        Fredericton?  Where's that?  See: http://www.fredericton.ca/       |
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